The invention concerns a tubular filter element for the filtration of fluids, the filter sheet or membrane has at least one layer and is folded in a plurality of axial folds, the end folds of which are connected in a leakproof manner in a hollow cylinder which is carried by an outer support grid and by an inner, perforated plastic support core on the outside of which the fold edges of the filter sheet are supported and the ends of which are enclosed by annular caps which enclose the front sides of the tubular filter sheet in a sealing manner. Such filter elements are known, for example, from DE-OS No. 31 28 546, DE-OS No. 21 02 510 and DE-GM No. 81 33 548.2. In known filter elements of this type the support core itself consists of a cylindrically formed grid with relatively sharp-edged perforations and with support ribs running circumferentially. The plurality of the fold edges come to lie against these support ribs during filtration as a result of the pressure gradient from the outside to the inside of the hollow cylindrical filter element. There is a danger in the case of sensitive filter materials that such could be damaged on the support core. An attempt has been made to avoid this by protecting and stabilizing the sensitive filter materials on both sides by a fine network. In addition to the task of supporting the filter, the support core also has the task of forming drainage pathways for the filtrate passing through the filter sheet from the closely pressed-together fold edges of the filter sheet. Both the outer support grid and the inner support core are enclosed at their ends by two caps which enclose the end edges of the folded tubular filter element by means of potting for example to achieve a good seal. Thus, the connection of the two caps is established via the tubular filter element connected therewith and usually via at least one of the two supports. Additional expansion forces affect the interconnected construction parts as a result of the dynamic forces acting on the entire filter element during filtration and as a result of stresses during extreme variations in temperature, e.g. during repeated autoclaving of the filter element for reasons of sterilization, so that these forces too must be taken into consideration during the construction of the filter element. The known filter elements of the art required improvement in this respect.